A suspension system of this type is described in German Pat. No. 4,234,217 A1. In this suspension system, very good suspension characteristics are realized due to the fact that the supplementary spring force influences the volume of the compressible medium inside of the piston-type accumulator, in addition to the normal volume changes caused by the load and the deflection and rebound movement, in such a way that a load ratio (or a compression and pressure ratio that deviates from the normal ratios that are present without a supplementary spring force), which differs from the load ratio of the strut, adjusts itself inside the piston-type accumulator. This altered accumulator load ratio is substantially smaller as compared to the load ratio of the strut. This measure allows the pressure accumulator to be constructed in a smaller and more compact fashion as well as with a shorter stroke of the separating piston. The supplementary spring force, in general, may be generated by means of arbitrary spring elements, but one of the known embodiments utilizes a pressure medium cylinder that acts upon the separating piston via the separating piston rod, whereby the pressure medium cylinder is connected with at least one pressure accumulator that generates a prestress pressure. This measure allows the desired variability of the supplementary spring force in a relatively simple fashion.